对称熵损失下的一类指数族刻度参数估计

In this paper we investigate the estimator for the rth power of the scale parameter in a class of exponential family under symmetric entropy loss L（θ, δ） = v（θ/δ ＋ δ/θ - 2）. An exact form of the minimum risk equivariant estimator under symmetric entropy loss is given, and the minimaxity of the minimum risk equivariant estimator is proved. The results with regard to admissibility and inadmissibility of a class of linear estimators of the form cT（X） ＋ d are given, where T（X） Gamma（v, θ）.     

A class of estimators of the mean survival time from interval censored data with application to linear regression

A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense that the estimators in a certain class have the same expectation as the mean survival time. The estimators have good properties such as strong consistency （with the rate of O（n^-1/1 （log log n）^1/2）） and asymptotic normality. The application to linear regression is considered and the simulation reports are given.     

Compressible navier-stokes equations with density-dependent viscosity, vacuum and gravitational force in the case of general pressure

This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.     

The BMO L space and Riesz transforms associated with Schrödinger operators

Let L =△ ＋ V be a SchrSdinger operator in Rd, d ≥ 3, where the nonnegative potential V belongs to the reverse HSlder class Sd. We establish the BMOL-boundedness of Riesz transforms З/ЗxiL-1/2, and give the Fefferman-Stein type decomposition of BMOL functions.     

Approximation by semigroup of spherical operators

This paper concerns about the approximation by a class of positive exponential type multiplier operators on the unit sphere Sn of the （n ＋ 1）- dimensional Euclidean space for n ≥2. We prove that such operators form a strongly continuous contraction semigroup of class （l0） and show the equivalence between the approximation errors of these operators and the K-functionals. We also give the saturation order and the saturation class of these operators. As examples, the rth Boolean of the generalized spherical Abel-Poisson operator ＋Vt^γ and the rth Boolean of the generalized spherical Weierstrass operator ＋Wt^k for integer r ≥ 1 and reals γ, k∈ （0, 1] have errors ｜｜＋r Vt^γ- f｜｜X ω^rγ（f, t^1/γ）X and ｜｜＋rWt^kf - f｜｜X ω^2rk（f, t^1/（2k））X for all f ∈ X and 0 ≤t ≤2π, where X is the Banach space of all continuous functions or all L^p integrable functions, 1 ≤p ≤＋∞, on S^n with norm ｜｜·｜｜X, and ω^s（f,t）X is the modulus of smoothness of degree s 〉 0 for f ∈X. Moreover, ＋r^Vt^γ and ＋rWt^k have the same saturation class if γ= 2k.     

Smallest close to regular bipartite graphs without an almost perfect matching

A graph G is close to regular or more precisely a （d, d ＋ k）-graph, if the degree of each vertex of G is between d and d ＋ k. Let d ≥ 2 be an integer, and let G be a connected bipartite （d, d＋k）-graph with partite sets X and Y such that ｜X｜- ｜Y｜＋1. If G is of order n without an almost perfect matching, then we show in this paper that·n ≥ 6d ＋7 when k = 1,·n ≥ 4d＋ 5 when k = 2,·n ≥ 4d＋3 when k≥3.Examples will demonstrate that the given bounds on the order of G are the best possible.     

A class of oscillatory singular integrals on triebel-lizorkin spaces

The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i｜x｜^aΩ（x）｜x｜^-n is studied,where a∈R,a≠0,1 and Ω∈L^1（S^n-1） is homogeneous of degree zero and satisfies certain cancellation condition. When kernel Ω（x＇ ）∈Llog＋L（S^n-1 ）, the Fp^a,q（R^n） boundedness of the above operator is obtained. Meanwhile ,when Ω（x） satisfies L^1- Dini condition,the above operator T is bounded on F1^0,1 （R^n）.     

$\alpha$-可分解4-圈系统

An m-cycle system of order v and index λ, denoted by m-CS（v,λ）, is a collection of cycles of length m whose edges partition the edges of λKv. An m-CS（v,λ） is α-resolvable if its cycles can be partitioned into classes such that each point of the design occurs in precisely α cycles in each class. The necessary conditions for the existence of such a design are m｜λv（v-1）/2,2｜λ（v -1）,m｜αv,α｜λ（v-1）/2. It is shown in this paper that these conditions are also sufficient when m = 4.     

Maximal regularity of second order delay equations in Banach spaces

Using known Ca-multiplier result, we give necessary and sufficient conditions for the second order delay equations：
u″（t）=Au（t）＋Fut＋Gu′＋f（t）,t∈R
to have maximal regularity in HSlder continuous function spaces C^α （R, X）, where X is a Banach space, A is a closed operator in X, F, G ∈L（C（[-r, 0], X）, X） are delay operators for some fixed r 〉 0.     

A Sufficient Condition for Rigidity in Extremality of Teichmuller Equivalence Classes by Schwarzian Derivative

The Strebel point is a TeichmOller equivalence class in the Teichmuller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper, we give a sufficient condition in terms of the Schwarzian derivative for a Teichmuller equivalence class of the universal Teichmuller space under which the class is a Strebel point. As an application, we construct a Teichmuller equivalence class that is a Strebel point and that is not an asymptotically conformal class.     

The ρ-variation of the Hermitian Riesz transform

In this paper we prove the behaviour in weighted Lp spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this operator maps LP（R, w（x）dx） into itself when w is a weight in the Ap class for 1 〈 p 〈 ∞. For p = 1 we get weak type for the A1 class. Weighted estimated are also obtained in the extreme case p = ∞.     

The 3D Inverse Problem of the Wave Equation for a General Multi-connected Vibrating Membrane with a Finite Number of Piecewise Smooth Boundary Conditions

The trace of the wave kernel μ（t） =∑ω=1^∞ exp（-itEω^1/2）, where {Eω}ω^∞=1 are the eigenvalues of the negative Laplacian -△↓2 = -∑k^3=1 （δ/δxk）^2 in the （x^1, x^2, x^3）-space, is studied for a variety of bounded domains, where -∞ 〈 t 〈 ∞ and i= √-1. The dependence of μ （t） on the connectivity of bounded domains and the Dirichlet, Neumann and Robin boundary conditions are analyzed. Particular attention is given for a multi-connected vibrating membrane Ω in Ra surrounded by simply connected bounded domains Ω j with smooth bounding surfaces S j （j = 1,……, n）, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components Si^＊ （i = 1 ＋ kj-1,……, kj） of the bounding surfaces S j are considered, such that S j = Ui-1＋kj-1^kj Si^＊, where k0=0. The basic problem is to extract information on the geometry Ω by using the wave equation approach from a complete knowledge of its eigenvalues. Some geometrical quantities of Ω （e.g. the volume, the surface area, the mean curvuture and the Gaussian curvature） are determined from the asymptotic expansion ofexpansion of μ（t） for small │t│.     

关于一类弱-Berwald的$(\alpha,\beta)$-度量

In this paper, we study an important class of （α,β）-metrics in the form F = （α＋β）^m＋1/α^m on an n-dimensional manifold and get the conditions for such metrics to be weakly- Berwald metrics, where α = √aij（x）y^iy^j is a Riemannian metric and β = bi（x）y^i is a 1-form and m is a real number with m ≠ -1,0,-1/n. Furthermore, we also prove that this kind of （α,β）-metrics is of isotropic mean Berwald curvature if and only if it is of isotropic S-curvature. In this case, S-curvature vanishes and the metric is weakly-Berwald metric.     

A Class of Generalized Hausdorff Means

In the research of divergent series the important idea is that choose a suitable trasformation have to be of regularity, of sequence of partial sum of the series. The Hausdorff transformation is H=δμδ in matrix form, in which μ is any diagonal transformation and δ is so-called δ-transformation. In this paper, we construct a class of generalized Housdorff transformation using the Gould-Hsu inverse series, and give necessary and sufficient condition of that it shou ld be regular.     

$K_v$的最大$K_2K_3$填充设计

Abstract Let Kv be the complete graph on v vertices, and G a finite simple undirected graph without isolated vertices. A G-packing of Kv, denoted by （v, G, 1）-packing, is a pair （X,A） where X is the vertex set of K＋ and ＋4 is a family of edge-disjoint subgraphs isomorphic to G in Kv. In this paper, the maximum number of subgraphs in a （v, G, 1）-packing is determined when G is K2 x K3, the Cartesian product of K2 and K3, leaving two orders undetermined. This design originated from the use of DNA library screening.     

Regular and Maximal Graphs with Prescribed Tripartite Graph as a Star Complement*

Let G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k ≥ 1. A star complement H for μ in G is an induced subgraph of G of order n-k with no eigenvalue μ, and the subset X = V(G-H) is called a star set for μ in G. The star complement provides a strong link between graph structure and linear algebra. In this paper, the authors characterize the regular graphs with K_2,2,s(s ≥ 2) as a star complement for all possible eigenvalues, the maximal graphs with K     

Approximately Linear Mappings in Banach Modules over a C^＊-algebra

Let X and Y be vector spaces. The authors show that a mapping f ： X →Y satisfies the functional equation 2d f（∑^2d j=1（-1）^j＋1xj/2d）=∑^2dj=1（-1）^j＋1f（xj） with f（0） = 0 if and only if the mapping f ： X→ Y is Cauchy additive, and prove the stability of the functional equation （≠） in Banach modules over a unital C^＊-algebra, and in Poisson Banach modules over a unital Poisson C＊-algebra. Let A and B be unital C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊- algebras. As an application, the authors show that every almost homomorphism h ： A →B of A into is a homomorphism when h（（2d-1）^nuy） =- h（（2d-1）^nu）h（y） or h（（2d-1）^nuoy） = h（（2d-1）^nu）oh（y） for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,.... Moreover, the authors prove the stability of homomorphisms in C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊-algebras.     

On the Non-Commutative Neutrix Product of the Distributions x＋^λ and x^＋μ

Let f and g be distributions and let gn = （g ＊ δn）（x）, where δn （x） is a certain converging to the Dirac delta function. The non-commutative neutrix product fog of f and g to be the limit of the sequence {fgn }, provided its limit h exists in the sense that sequence is defined N-lim n-∞（f（x）g,, （x）, φ（x）〉 = （h（x）, φ（x）},for all functions p in 2. It is proved that （x^λ＋1n^px＋）0（x^μ＋1n^qx＋）=x＋^λμ1n^p＋qx＋,（x^λ-1n^qx-）=x-^λ＋μ1n^p＋qx-,for λ＋μ〈-1; λ,μ, λ＋μ≠-1,-2…and p,q=0,1,2……     

A Sufficient Condition for Rigidity in Extremality of Teichmller Equivalence Classes by Schwarzian Derivative

The Strebel point is a Teichm ¨uller equivalence class in the Teichm ¨uller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper,we give a sufficient condition in terms of the Schwarzian derivative for a Teichm ¨uller equivalence class of the universal Teichm ¨uller space under which the class is a Strebel point. As an application, we construct a Teichm ¨uller equivalence class that is a Strebel point and that is not an asymptotically conformal class.     

Intersections and polar functions of fractional brownian sheets

Let B^H={B^H（t）,t∈R^N＋}be a real-valued（N,d）fractional Brownian sheet with Hurst index H=（H1,…,HN）.The characteristics of the polar functions for B^H are discussed.The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of B^H is obtained.The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for B^H are presented.Furthermore,it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions.A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Holder condition is also solved.